Example 1: balancing
A 500 N parent sits 1.2 m from the pivot of a seesaw. Where must a 300 N child sit to balance?
- Anticlockwise moment = 500 × 1.2 = 600 N m.
- Distance = 600 ÷ 300 = 2.0 m on the other side.
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IB DemystifiedMYP Sciences
Moments and levers
A seesaw balances a small child and a larger one; a long spanner loosens a stubborn nut; a crane lifts steel beams without tipping over. All of these depend on moments, the turning effects of forces, and on the simple rule that balances them.
Recommended for MYP 3 · About 3 lessons · Criteria A, B, C and D
On this page
- Learning objectives
- Before you start
- Key vocabulary
- Understanding the ideas
- Working with moments
- Moments in the real world
- Worked examples
- Assessment tips
- Check your understanding
- Practice questions
- Investigation
- Criterion-linked questions
- Challenge questions
- Topic check
- Review your mistakes
- Your progress
Learning objectives
By the end of this topic you should be able to:
- calculate the moment of a force
- apply the principle of moments to balanced objects
- explain how levers and tools reduce the force needed
- explain centre of mass, stability and toppling
- analyse balancing data and design fair experiments
- discuss lifting tools for workers and crane safety
Before you start
You will use these skills. If any feel shaky, review them first.
- forces and weight (see Forces and their effects and Newton's laws of motion)
- measuring distances and converting cm to m
- rearranging simple equations
Key vocabulary
- Moment
- The turning effect of a force: force × perpendicular distance from the pivot.
- Pivot
- The point about which something turns.
- Principle of moments
- For a balanced object, total clockwise moment = total anticlockwise moment.
- Lever
- A rigid bar that turns about a pivot, used to change the size of a force.
- Centre of mass
- The point where the whole weight of an object seems to act.
- Stable
- Hard to topple, usually because of a low centre of mass and wide base.
Understanding the ideas
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Moments
A force can make an object turn about a pivot. The turning effect is called a moment: moment = force × perpendicular distance from the pivot, measured in newton metres (N m). The same force has a larger moment further from the pivot.
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The principle of moments
When an object is balanced, the total clockwise moment equals the total anticlockwise moment. This principle of moments lets us calculate unknown forces or distances, from seesaws to cranes.
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Levers
Levers use moments to change forces. In a wheelbarrow, a bottle opener or a spanner, a small effort far from the pivot can balance a large load close to it, although the effort must move further.
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Centre of mass and stability
Every object has a centre of mass. If the line of its weight falls outside its base, the weight's moment tips it over. Low, wide objects are more stable, which is why buses, cranes and racing cars are designed as they are.
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What does it connect to?
Moments link to forces and Newton's laws, work and energy, and the human skeleton, where bones act as levers moved by muscles.
Working with moments
- Moment = force (N) × perpendicular distance from pivot (m), in N m.
- Balanced: total clockwise moment = total anticlockwise moment.
- Levers: a longer distance means a smaller force for the same moment.
- Stability: a low centre of mass and a wide base make objects harder to topple.
- Units: convert cm to m before calculating in N m.
Moments in the real world
Tower cranes use huge counterweights to balance their loads. Wheelbarrows and hand trolleys help construction workers move heavy materials with less strain. Door handles are placed far from the hinges so doors open easily.
Worked examples
Example 2: a spanner
A nut needs a moment of 24 N m to loosen it. What force is needed on a 0.30 m spanner?
- Force = moment ÷ distance.
- 24 ÷ 0.30 = 80 N.
Assessment tips
Questions on moments often use diagrams of beams, levers and tools. Expect to:
- Calculate moments, forces and distances, with units.
- Apply the principle of moments with one or more forces on each side.
- Explain levers and stability.
- Analyse balancing data and design fair tests.
Common mistakes: forgetting to convert cm to m; using the distance along a slanted force instead of the perpendicular distance; comparing forces instead of moments; and forgetting that longer levers need more movement.
Check your understanding
Quick questions on the ideas above. Try each one before using a hint.
Practice questions
Investigation: weighing with a metre rule
Partially guided investigation · about 40 minutes · pairs
- Research question
- Can the principle of moments be used to find the weight of an unknown object?
- Scientific background
- If a metre rule is balanced at its centre, the moment of a known weight on one side equals the moment of the unknown weight on the other: W_unknown × d_unknown = W_known × d_known.
- Hypothesis
- Write your own prediction, with a scientific justification.
- Variables
- Identify your independent, dependent and control variables, and explain how you will control them.
- Apparatus
- Metre rule, pivot (such as a triangular block or a clamp through the 50 cm hole), known weights (1 N, 2 N), an unknown object (such as a stone or a bunch of keys) on a loop of thread, newton meter for checking.
- Method
- Balance the rule at its centre of mass.
- Hang the unknown object at a fixed distance on one side, such as 15 cm.
- Move a known weight on the other side until the rule balances, and record its distance.
- Calculate the unknown weight, repeat with different distances, and check with a newton meter.
Safety. Keep weights over the table so they cannot fall on feet. Do not lean on the rule.
Then evaluate: how close was your calculated value to the newton meter reading, and what caused any difference?
Criterion-linked questions
Criterion B: inquiring and designing
Criterion C: processing and evaluating
Criterion D: reflecting on the impacts of science
Challenge questions
Harder problems in unfamiliar contexts. Plan before you calculate.
Topic check
Five questions picked at random from the whole topic. Take a new set whenever you like.
Review your mistakes
Questions you got wrong on this device appear here so you can try them again. Answer one correctly and it leaves the list.
Your progress
Tracked separately for each skill, on this device only.
| Skill | Correct | Status |
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